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Introduction

  • Kris L. G. Heyde

Abstract

Approaching the atomic nucleus at low excitation energy (excitation energy less than the nucleon separation energy) can be done on a non-relativistic level. If we start from an A-nucleon problem interacting via a given two-body potential V i, j, the non-relativistic Hamiltonian can be written as
$$H = \sum\limits_{i = 1}^A {t_2 + \frac{1}{2}\sum\limits_{i,j = 1}^A {V_{i,j} } } ,$$
where t i is the kinetic energy of the nucleon motion. Much experimental evidence for an average, single-particle independent motion of nucleons exists, a point of view that is not immediately obvious from the above Hamiltonian. This idea acts as a guide making a separation of the Hamiltonian into A one-body Hamiltonians (described by an average one-body potential U i) and residual interactions. This can be formally done by writing
$$H = {{H}_{0}} + {{H}_{{res}}}$$
, with
$${{H}_{0}} = \sum\limits_{{i = 1}}^{A} {\left\{ {{{t}_{i}} + {{U}_{i}}} \right\}}$$
, and
$${{H}_{{res}}} = \tfrac{1}{2}\sum\limits_{{i,j = 1}}^{A} {{{V}_{{i,j}}}} - \sum\limits_{{i = 1}}^{A} {{{U}_{i}}}$$
. It is a task to determine U i as well as possible such that the residual interaction H res remains as a small perturbation on the independent A-nucleon system. This task can be accomplished by modern Hartree-Fock methods where the residual interaction with which one starts is somewhat more complicated such as the Skyrme-type interactions (two-body plus three-body terms) which have been used with considerable success. This process of going from the two-body interaction V i, j towards a one-body potential is drawn schematically.

Keywords

Residual Interaction Interact Boson Model Nuclear Shell Model Harmonic Oscillator Wave Function Nucleon Separation Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Kris L. G. Heyde
    • 1
  1. 1.Laboratorium voor Theoretische Fysica en Laboratorium voor Kernfysica, Vakgroep Subatomaire en StralingsfysicaUniversiteit GentGentBelgium

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